As most of you know probably know by now, round 2 of Apple’s US patent battle with Samsung kicked off this week in a San Jose, California court room. The last time these 2 companies met on American soil, in the fall of 2012, Apple was awarded $1 billion in damages.

This time around, the iPad-maker is asking for twice that much. And although it’s using different patents, and going after different Samsung devices, it’s ultimately trying to prove the same thing as it did before: that Samsung intentionally copied its patented inventions…

The honorable US District Court Lucy H. Koh will once again be presiding over the case, which will be decided by a jury of four women and four men, who were chosen Monday. Apple is suing Samsung over five patents, and Samsung is countersuing over two patents.

Apple Patents

-U.S. Patent No. 5,946,647 for a “System and method for performing an action on a structure in computer-generated data”-U.S. Patent No. 6,847,959 for a “Universal interface for retrieval of information in a computer system”-U.S. Patent No. 7,761,414 for “Asynchronous data synchronization amongst devices” -U.S. Patent No. 8,046,721 for “Unlocking a device by performing gestures on an unlock image”-U.S. Patent No. 8,074,172 for a “Method, system, and graphical user interfacefor providing word recommendation”

“The evidence in this case will be that Samsung copied the iPhone and it also took many other Apple inventions that had not yet appeared in Apple products,” Apple attorneyHarold McElhinny said during its opening arguments. Apple is seeking as much as $2 billion in damages, saying that various Samsung phones and tablets infringed on five of its patents.

McElhinny began his opening statement Tuesday, much as Apple did in that prior case, showing reviews and praise heaped upon the iPhone as well as snippets from Steve Jobs’ January 2007 iPhone introduction at Macworld. Apple also plans to show various internal Samsung documents, some of which it previewed on Tuesday, that it says demonstrate that Samsung knew it was violating Apple’s intellectual property.

Apple alleges that Samsung sold 37 million infringing phones and tablets in the US, and it’s looking for lost profits from those products as well as ‘reasonable royalties’ on remaining ones. The company is seeking an average of $33 per device, and as much as $40 per device.

Slide from the first Samsung vs. Apple trial

Meanwhile, Samsung’s strategy this time around is to downplay the value of intellectual property in general. It actually went out and purchased the two patents that it’s counter-suing Apple with, and is asking for less than $7 million in damages. That’s a bold strategy Cotton.

Anyway, the next day in court will be Friday of this week, and the case will likely last a month. Expect to see executives from both companies (maybe even the ousted Scott Forstall) testify in the coming weeks, secrets revealed, and much more in this high-profile patent trial.